We analyze the obtained solutions of the non-linear Shroedinger equation for spherically and axially symmetrical electrons density oscillations in plasma. The conditions of the oscillations process existence are examined. It is shown that in the center or on the axis of symmetry of the systems the static density of electrons enhances. This process results in the increasing of density and pressure of the ion gas. We suggest that this mechanism could occur in nature as rare phenomenon called the fireball and could be used in carrying out the research concerning controlled fusion. The description of the experiments, carried out for the purpose to generate long-lived spherical plasma structures, is presented.